In section 2.2 of Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity (http://arXiv.org/abs/1308.1697), beneath equation (2.9), it is mentioned that $u^{\pm}=v^{\mp}$, where $u^\pm$ are massless spinors corresponding to helicity eigenstates for particles, and $v^\mp$ are those for antiparticles.

Why is this true in general? Or is it a just a convention for associating certain antiparticle spinors with particle spinors? From equation (3.136) in section 3.6 of Peskin and Schroeder, we have$$v^s(p)=\begin{pmatrix}\sqrt{p\cdot\sigma}\xi^{-s}\\-\sqrt{p\cdot\bar{\sigma}}\xi^{-s}\end{pmatrix},$$ which seems to suggest that it is just a matter of choosing some basis of two-component spinors $\xi^{-s}$, which in this case happen to have opposite spin from those used in $u^{s}(p)$. With this choice of $v^s(p)$, it is straightforward to get $u^{\pm}=v^{\mp}$ in the massless limit.

I am sure that there is some physical justification for this but what is it? Elvang and Huang suggests using crossing symmetry but the choice of relating s and t channel diagrams seems as arbitrary as any convention.


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